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Chemistry
Chemistry
Problem
For a hydrogen-like ion of atomic number
Z
Z
Z
, which expression gives the radius
r
n
r_{n}
r
n
of the nth orbit? a)
r
n
=
4
π
ε
0
ℏ
2
m
e
2
n
2
r_{n}=\dfrac{4\pi\varepsilon_{0}\hbar^{2}}{me^{2}}\,n^{2}
r
n
=
m
e
2
4
π
ε
0
ℏ
2
n
2
b)
r
n
=
4
π
ε
0
ℏ
2
m
e
2
n
Z
r_{n}=\dfrac{4\pi\varepsilon_{0}\hbar^{2}}{me^{2}}\,\dfrac{n}{Z}
r
n
=
m
e
2
4
π
ε
0
ℏ
2
Z
n
c)
r
n
=
4
π
ε
0
ℏ
2
m
e
2
n
2
Z
r_{n}=\dfrac{4\pi\varepsilon_{0}\hbar^{2}}{me^{2}}\,\dfrac{n^{2}}{Z}
r
n
=
m
e
2
4
π
ε
0
ℏ
2
Z
n
2
d)
r
n
=
4
π
ε
0
ℏ
2
m
e
2
n
2
Z
2
r_{n}=\dfrac{4\pi\varepsilon_{0}\hbar^{2}}{me^{2}}\,\dfrac{n^{2}}{Z^{2}}
r
n
=
m
e
2
4
π
ε
0
ℏ
2
Z
2
n
2
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